Why use R

• It is relatively easy to program. More data- and statistics- oriented than Python
• A very well maintained Package repository: if a statistical technique exists, bet that there is an R-package
• R has a very active community, which means quality control, efficient bug tracking and fixing, and regular updates
• It’s relatively easy to create complex graphs
• Literate programming: straight from data analysis to publication

Graphical display of data using R

The anatomy of an R-expression

log(2.71)

[1] 0.9969486

• log(2.71): an expression
• log(): a function or method
• 2.71: an argument of the function log()
• 0.9969486: the output of the expression
• 2.71, 0.9969486: are objects (of class numeric)

The anatomy of another R-expression

1 + 2

[1] 3

• 1 + 2: an expression
• '+'(): a function or method
• 1 and 2: are arguments of the function '+'()
• 1 and 2: are objects (of class numeric)

'+'(1,2)

[1] 3

R is an object oriented language

• All objects belong to a class
• Classes are organized in a class hierarchy
• Objects have associated methods

sex <- factor(c("M","F","F","M","M","M"))
sex

[1] M F F M M M
Levels: F M

as.numeric(sex)

[1] 2 1 1 2 2 2

Object class hierarchy in R

Note that these are the basic classes. Packages may introduce new child classes of basic classes.

Data objects in R

Every data object in R is derived from the vector class

• vector is an abstract class in R, representing a tuple, a set of containers that carry an index number:

Atomic vectors

numeric vector: every element contains a single number

1

[1] 1

seq(1,5)

[1] 1 2 3 4 5

1:5

[1] 1 2 3 4 5

rep(c(1,3),5)

 [1] 1 3 1 3 1 3 1 3 1 3

rnorm(5)

[1] -0.28206602 -0.10055451 -0.03093558 -1.47619504 -0.74812609

Quiz: functions and arguments

In the expressions seq(1,5) and 1:5

• What are the functions/methods?
• What is/are the argument(s)?
• What is the class of the argument(s)?
• What is the class of the output of the functions?

character vector: each element holds a single character string

"a"

[1] "a"

'Abc'

[1] "Abc"

letters

 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s"
[20] "t" "u" "v" "w" "x" "y" "z"

logical vector: each element holds a single logical value

1==1

[1] TRUE

1==2

[1] FALSE

c('male','female','female','male') == 'male'

[1]  TRUE FALSE FALSE  TRUE

Creating a vector

Use the concatenation function c() to create vectors with arbitrary data

c(15.3,11.4,12.5,13.1)

[1] 15.3 11.4 12.5 13.1

c('a','b','c')

[1] "a" "b" "c"

c('a','b','sample')

[1] "a"      "b"      "sample"

Quiz: functions, input and output classes

In the expression c('a','b','sample')

• How many arguments does the function c() take?

• What is the class of the argument(s)?

• What is, in general, the class of the output of the function c()?

• How many arguments does the outer concatenation in c(c('a','b'),'sample') take? What will be the output?

Two types of base functions in R

All functions have vectors as arguments. How do they operate on vectors?

c(1,2,3) + c(5,6,7)

[1]  6  8 10

c(1,2,3,4) + c(1,2)

[1] 2 4 4 6

c(1,2,3) + 1

[1] 2 3 4

c(1,2,3) > 2

[1] FALSE FALSE  TRUE

mean(c(1,2,3))

[1] 2

sd(c(1,2,3))

[1] 1

sum(c(1,2,3))

[1] 6

any(c(FALSE, FALSE, FALSE, TRUE, FALSE))

[1] TRUE

Storing objects in memory

Giving an object a name with the assignment operator <- creates a semi-permanent copy in memory

mydata <- c(15.3,11.4,12.5,13.1)

mydata

[1] 15.3 11.4 12.5 13.1

mean(mydata)

[1] 13.075

sd(mydata)

[1] 1.641899

Generating and storing a vector with random numbers

sample <- runif(100)

sample

  [1] 0.321652743 0.255329920 0.813072467 0.844754566 0.741460668 0.452447160
  [7] 0.660586335 0.884833407 0.376626137 0.396120389 0.203076562 0.613253285
 [13] 0.755529126 0.082694459 0.340706577 0.261525724 0.256461629 0.236181747
 [19] 0.477760768 0.450746441 0.475976889 0.247493265 0.983040848 0.634353817
 [25] 0.516292815 0.764290652 0.625141596 0.249894288 0.612004598 0.850249073
 [31] 0.996369231 0.276770240 0.553375643 0.425778985 0.279011318 0.575475608
 [37] 0.547314094 0.776472423 0.786281534 0.458755063 0.392587437 0.984401637
 [43] 0.952639495 0.609412803 0.075744548 0.792524322 0.748155368 0.870700320
 [49] 0.610821505 0.919262931 0.037285194 0.157941364 0.565128270 0.973846421
 [55] 0.337083640 0.220714435 0.775216294 0.264685093 0.834163542 0.709327108
 [61] 0.073919139 0.942226410 0.581857634 0.656319579 0.583717612 0.630195420
 [67] 0.287243839 0.524404053 0.693821546 0.727689154 0.184470702 0.592739058
 [73] 0.511415237 0.135698926 0.551563792 0.117924483 0.231563725 0.218273374
 [79] 0.393647147 0.320536121 0.083605645 0.269399869 0.679423194 0.937780983
 [85] 0.871313597 0.787220405 0.879004461 0.470023791 0.702892255 0.409319881
 [91] 0.632400250 0.077210962 0.356680507 0.142912854 0.976355729 0.033196826
 [97] 0.001373154 0.676875147 0.427970793 0.778332553

Real life: missing data

Elements of any atomic type of vector can have the value NA: not available

• NA is not the same as 0 or ""

mydata <- c(15.3,11.4,NA,13.1)
mydata + 1

[1] 16.3 12.4   NA 14.1

mean(mydata)

[1] NA

mean(mydata, na.rm=TRUE)

[1] 13.26667

Real life: avoiding program exit upon numerical errors

• Inf, -Inf: resulting from division by 0 or from calculations beyond the numeric capacity of the computer

mydata <- c(15.3,11.4,0,13.1)

1/mydata

[1] 0.06535948 0.08771930        Inf 0.07633588

mydata <- c(15.3,11.4,0,13.1)

0/mydata

[1]   0   0 NaN   0

Quiz: simulate 100 rolls with a fair die

• create one or two R-statements
• required output: a vector of 100 random numbers from the set 1..6
• all numbers must have equal probability to be drawn
• use, for example
  • sample() or sample.int()
  • help() for these functions

factor: each element holds a single discrete value

factor: a vector with a limited vocabulary

gender <- factor(c("Male", "Female", "Female", "Male"))

gender

[1] Male   Female Female Male  
Levels: Female Male

class(gender)

[1] "factor"

as.numeric(gender)

[1] 2 1 1 2

array: a vector with an attribute

array: consists of an atomic vector. Special case: matrix, a 2-dimensional array

v <- 1:4

class(v)

[1] "integer"

attributes(v)

NULL

mymat <- matrix(v, ncol=2)

mymat

     [,1] [,2]
[1,]    1    3
[2,]    2    4

attributes(mymat)

$dim
[1] 2 2

data.frame: the equivalent of a table

• Elements in a data.frame correspond to columns
• The elements contain vectors
• Vectors inside the elements of a data.frame must all have equal length

d <- data.frame(
  gender = factor(c("M","F","F", "M")),
  weight = c(69.1,56.4,61.0,81.5)
)

d

  gender weight
1      M   69.1
2      F   56.4
3      F   61.0
4      M   81.5

d$weight

[1] 69.1 56.4 61.0 81.5

mean(d$weight)

[1] 67

Methods: statistics made easier

plot(d, col='steelblue')

t.test(weight~gender, data=d)

    Welch Two Sample t-test

data:  weight by gender
t = -3.4717, df = 15.944, p-value = 0.00316
alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
95 percent confidence interval:
 -17.014143  -4.110979
sample estimates:
mean in group Female   mean in group Male 
            67.44078             78.00334 

Two equivalent ways to take an object out of an element

1. The $ operator works with named indexes:

d$weight

 [1] 72.93805 91.13514 73.61649 64.29421 84.09792 71.75040 81.99970 73.98459
 [9] 82.68189 83.53499 68.73414 73.21086 66.80506 69.45581 66.43022 72.51171
[17] 60.32600 73.96749 65.76018 57.20630

d[['weight']]

 [1] 72.93805 91.13514 73.61649 64.29421 84.09792 71.75040 81.99970 73.98459
 [9] 82.68189 83.53499 68.73414 73.21086 66.80506 69.45581 66.43022 72.51171
[17] 60.32600 73.96749 65.76018 57.20630

d[[2]]

 [1] 72.93805 91.13514 73.61649 64.29421 84.09792 71.75040 81.99970 73.98459
 [9] 82.68189 83.53499 68.73414 73.21086 66.80506 69.45581 66.43022 72.51171
[17] 60.32600 73.96749 65.76018 57.20630

R packages

• A package is a coherent set of
  • class definitions
  • functions operating on these classes
  • examples of the use of these classes
• These are packaged in a single file that, after installation of the package, results in a library folder with several files
  • Look into the library subdirectory of the R installation directory (but don’t mess with it)

R packages

• A number of packages is loaded at start-up of R
  • They contain definitions of commonly used data structures and functions
• Other packages are loaded on-demand by the user with functions
  • library(packagename)
  • require(packagename)

Examples of R-packages

• Loaded at start-up
  • base: all basic classes and functions used in R, including basic statistical functions
  • stats: classes and functions for more advanced statistical operations
• Loaded on demand
  • edgeR: classes and functions for RNAseq analysis
  • ggplot2: classes and functions for advanced graphics

Graphical systems

plot(x=iris$Petal.Length, y=iris$Sepal.Length, 
     asp=1,
     xlab="Petal length (cm)", ylab="Sepal length (cm)", 
     col=c('maroon','plum3','navyblue')[iris$Species],
     pch = 19
     )
lines(x=c(1,7),y=c(4.31+0.41*1, 4.31+0.41*7), lwd=2, col='red')
legend(1.2, 8,
       pch=19,
       col=c('maroon','plum3','navyblue'), 
       legend=levels(iris$Species))

ggplot(data=iris, mapping=aes(x=Petal.Length, y=Sepal.Length, colour=Species)) +
  labs(x='Petal length (cm)', y='Sepal length (cm)') +
  stat_smooth(method=lm, se=FALSE, colour="red") +
  geom_point(size=3) + 
  theme(legend.position=c(0.05,0.95), legend.justification=c(0,1)) +
  scale_color_manual(values=c('maroon','plum3','navyblue'))

Data processing

Example: Sepal width and length means and standard deviations per species

    Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
1            5.8         2.7          4.1           1 versicolor
2            6.4         2.8          5.6         2.1  virginica
3            4.4         3.2          1.3         0.2     setosa
..            ..          ..           ..          ..         ..
150          6.1         2.8            4         1.3 versicolor

means <- do.call(rbind, lapply(iris[,c("Sepal.Length", "Sepal.Width")], function(x) {tapply(x, iris$Species, mean)}))
sds <- do.call(rbind, lapply(iris[,c("Sepal.Length", "Sepal.Width")], function(x) {tapply(x, iris$Species, sd)}))
rownames(means) <- paste0(rownames(means), "_avg")
rownames(sds) <- paste0(rownames(sds), "_sd")
df <- as.data.frame(rbind(means,sds))
df

                    setosa versicolor virginica
Sepal.Length_avg 5.0060000  5.9360000 6.5880000
Sepal.Width_avg  3.4280000  2.7700000 2.9740000
Sepal.Length_sd  0.3524897  0.5161711 0.6358796
Sepal.Width_sd   0.3790644  0.3137983 0.3224966

iris |>
  group_by(Species) |>
  select(starts_with("Sepal")) |>
  summarise(across(where(is.numeric), list(avg=mean, sd=sd))) |>
  flextable()

Integrating text and code

Several flavors and purposes

• Literate programming: focus on programming logic
• Documentation generation: focus on program documentation
• RMarkdown, Quarto: focus on scientific and technical document generation

Quarto documents

The weaving process

Functions

Functions do things with the input

• Input: function arguments (can be one or several objects)
• Output: result of a function (exactly one object)

R contains many pre-defined functions, you saw mean, sd, sum, t.test

add <- function(a,b) {
  result = a+b
  return(result)
}

add(4,3)

[1] 7

Programming

if (a > b) {
  print(a - b)
} else {
  print(b - a)
}

for (i in 1:10) {
   print(i*i)
}

[1] 1
[1] 4
[1] 9
[1] 16
[1] 25
[1] 36
[1] 49
[1] 64
[1] 81
[1] 100